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Chapter 1: Problem 70

Find the value of each expression. $$ 6(5-8) \div 9+4 $$

Short Answer

Expert verified
The value of the expression is 2.

Step by step solution

01

Simplify Inside the Parentheses

Begin by solving the expression inside the parentheses: \(5 - 8\). This simplifies to \(-3\).
02

Multiply by 6

Next, multiply the result from Step 1 by 6: \(6 \cdot (-3) = -18\).
03

Divide by 9

Take the result from Step 2 and divide it by 9: \(-18 \div 9 = -2\).
04

Add 4

Finally, add 4 to the result from Step 3: \(-2 + 4 = 2\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Parentheses
When solving mathematical expressions, it's important to handle operations inside parentheses first. Parentheses indicate that the operations within should be completed before anything else in the expression.
This is a fundamental rule in the order of operations in mathematics, often remembered by the acronym PEMDAS or BIDMAS (Brackets first, Orders (i.e., powers and square roots, etc.), Division and Multiplication (left-to-right), Addition and Subtraction (left-to-right)).
  • Look for any expressions inside parentheses and solve them first.
  • This step simplifies the equation, setting the stage for solving the remaining parts efficiently.
  • Mistakenly neglecting parentheses can lead to incorrect results, since they often change the order in which calculations are performed.

In the given exercise, the expression \(5 - 8\) inside the parentheses is solved first to get \(-3\). By starting here, we ensure that the rest of the operations are based on accurate calculations.
Multiplication and Division
Next in line are multiplication and division, which should be addressed from left to right as they appear in the expression. These operations have equal precedence, so you process them in the order they come.
  • After solving expressions inside parentheses, move on to multiplication and division.
  • Handle them as you encounter them, moving left to right through the equation, without skipping to addition or subtraction prematurely.
  • These steps further simplify the expression into a more manageable form.

In our step-by-step solution:
  • We first multiply the result of the parentheses: \(6 \cdot (-3) = -18\), and then,
  • We divide that result by 9: \(-18 \div 9 = -2\).
Performing these calculations in this order correctly simplifies the problem, allowing us to move efficiently towards the final solution.
Addition and Subtraction
Finally, after handling all parentheses, multiplication, and division, proceed with addition and subtraction. These operations, like multiplication and division, should be performed from left to right.
  • Addition and subtraction are the last operations to complete.
  • Carefully move from left to right, ensuring that you apply each operation correctly based on its place in the expression.
  • This brings the entire calculation to a close, revealing the answer.

In the exercise:
  • We add 4 to the previously calculated result: \(-2 + 4 = 2\).
By approaching the expression step by step, following the order of operations, we accurately arrive at the final value of the expression, which is 2.

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Most popular questions from this chapter

Solve each equation. Check your solutions. \(|x|=7\)

Write a compound inequality for which the graph is the empty set.

For Exercises \(46-49,\) use the following information. You can use the operators in the LOGIC menu on the TI-83/84 Plus to graph compound and absolute value inequalities. To display the LOGIC menu, press 2nd Test. A graphing calculator can also be used to solve absolute value inequalities. Write the expression you would enter for \(Y 1\) to find the solution set of the inequality \(|2 x-6| > 10 .\) Then use the graphing calculator to find the solution set. (Hint: The absolute value operator is item 1 on the MATH NUM menu.)

Solve each inequality. Then graph the solution set on a number line. \(\frac{4 x+2}{6}<\frac{2 x+1}{3}\)

Solve each inequality. Graph the solution set on a number line. $$ |w| \geq-2 $$
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